A têmpera controlada pela entropia : uma caracterização formal

Universidade de Aveiro Departamento de Matemática 1999

António José Batel Anjo

A Têmpera Controlada pela Entropia Uma caracterização formal

dissertação apresentada à Universidade de Aveiro para cumprimento dos requisitos necessários à obtenção do grau de Doutor em Matemática. Trabalho realizado sob a orientação científica da Prof. Doutora Maria Rosália Dinis Rodrigues, Professora Auxiliar do Departamento de Matemática da Universidade de Coimbra

o júri presidente

Reitor da Universidade de Aveiro

vogais António Dias de Figueiredo Professor Catedrático da Faculdade de Ciências e Tecnologia da Universidade de Coimbra Maria Beatriz Fernandes Matias Professora Associada da Universidade de Aveiro Domingos Moreira Cardoso Professor Associado da Universidade de Aveiro Helena Ramalhinho Lourenço Professora Auxiliar do Departamento d'Economia i Empresas da Universidad Pompeu Fabra, Barcelona, Espanha Maria Rosália Dinis Rodrigues Professora Auxiliar da Faculdade de Ciências e Tecnologia da Universidade de Coimbra (Orientadora)

agradecimentos

À Prof. Rosália pela forma como conduziu a orientação deste trabalho, em que a amizade e a liberdade de pensamento estiveram sempre presentes. À Paula Carvalho e ao Prof. David Vieira pela leitura atenta deste trabalho e por todo o apoio ao longo destes anos. À Andreia Hall, Luís Comparada, Ana Maria Almeida e Manuel Rodrigues pela dedicação com que leram este trabalho. À Auzira Bettencourt por ter estado presente em todos os momentos. À Maria João e à Rosa Elisa por terem estado, efectivamente, presentes em todos os momentos. À Zhang Yulin pelo desenho do caracter que se encontra na capa e que representa a Entropia.

resumo

Nesta dissertação é proposto um modelo para a Têmpera Simulada, como abordagem metaheurística para a resolução de problemas de Optimização Combinatória. O modelo é construído tendo por base o conceito de Entropia entendido no contexto da Teoria da Informação. Para este modelo é feita uma caracterização formal e são estabelecidas propriedades a partir das quais se demonstram diversos resultados. A partir deste modelo são deduzidos algoritmos adaptáveis e gerados automaticamente em tempo real. São apresentados testes computacionais da aplicação de um algoritmo assim construído ao Problema do Caixeiro Viajante.

abstract

In this dissertation a new model for Simulated Annealing is presented, as a meta-heuristic approach to Combinatorial Optimisation problems. The model is built upon the concept of Entropy, in the sense of Information Theory. A formal characterisation is established and several results, such as the asymptotic convergence of the method, are proved. A class of algorithms is them derived from the model, which are adaptable and automatically generated in running time. Computational results of the application of a simple algorithm of that class, where applied to the Travelling Salesman Problem, are also reported.

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